Problem: Simplify the following expression: $\sqrt{13}+\sqrt{117}+\sqrt{52}$
Answer: First, try to factor any perfect squares out of the radicals. $= \sqrt{13}+\sqrt{117}+\sqrt{52}$ $= \sqrt{13}+\sqrt{9 \cdot 13}+\sqrt{4 \cdot 13}$ Separate the radicals and simplify. $= \sqrt{13}+\sqrt{9} \cdot \sqrt{13}+\sqrt{4} \cdot \sqrt{13}$ $= \sqrt{13}+3\sqrt{13}+2\sqrt{13}$ Finally, simplify by combining the terms. $= ( 1 + 3 + 2 )\sqrt{13} = 6\sqrt{13}$